1. The problem statement, all variables and given/known data I'm getting different results when choosing my u & dv for Integration by Parts on the following integral: [tex]\int 2x^3 e^x^2 dx [/tex] (Note, the exponent on 'e' is x^2) This yields the correct solution: u = [tex]x^2[/tex] dv = [tex]2x e^x^2 dx [/tex] du = [tex]2xdx[/tex] v = [tex]e^x^2[/tex] However, I have tried using this instead (*) u = [tex]2x^3[/tex] dv = [tex]e^x^2 dx [/tex] du = [tex]6x^2 dx[/tex] v = [tex](e^x^2) / 2x[/tex] and this is yielding the incorrect solution (see 3.) 2. Relevant equations Integration by Parts: [tex]\int udv = uv - \int vdu [/tex] 3. The attempt at a solution The correct solution turns out to be [tex] x^2 e^x^2 - e^x^2 + C[/tex] When I use my other choice of variables (*), I get (using IBP) [tex] \int 2x^3 e^x^2 dx = 2x^3 e^x^2 / 2x - \int e^x^2 / 2x * 6x^2 dx [/tex] which leads to: [tex]x^2 e^x^2 - 3/2 e^x^2 + C [/tex] which is different from the other choice of variables. I've looked over both choices of variables, and I don't know why the second choice (*) comes up with a different solution. Thanks for the help!